Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distribution

Access Full Article

Abstract

top
The problem of estimating the number, n, of trials, given a sequence of k independent success counts obtained by replicating the n-trial experiment is reconsidered in this paper. In contrast to existing methods it is assumed here that more information than usual is available: not only the numbers of successes are given but also the number of pairs of consecutive successes. This assumption is realistic in a class of problems of spatial statistics. There typically k = 1, in which case the classical estimators cannot be used. The quality of the new estimator is analysed and, for k > 1, compared with that of a classical n-estimator. The theoretical basis for this is the distribution of the number of success pairs in Bernoulli trials, which can be determined by an elementary Markov chain argument.

@article{Kühne1994, abstract = {The problem of estimating the number, n, of trials, given a sequence of k independent success counts obtained by replicating the n-trial experiment is reconsidered in this paper. In contrast to existing methods it is assumed here that more information than usual is available: not only the numbers of successes are given but also the number of pairs of consecutive successes. This assumption is realistic in a class of problems of spatial statistics. There typically k = 1, in which case the classical estimators cannot be used. The quality of the new estimator is analysed and, for k > 1, compared with that of a classical n-estimator. The theoretical basis for this is the distribution of the number of success pairs in Bernoulli trials, which can be determined by an elementary Markov chain argument.}, author = {Kühne, Wolfgang, Neumann, Peter, Stoyan, Dietrich, Stoyan, Helmut}, journal = {Applicationes Mathematicae}, keywords = {n-estimator; simulation; silicon wafer; Markov chain; binomial distribution; spatial statistics; -estimator; number of success pairs; Bernoulli trials}, language = {eng}, number = {3}, pages = {331-337}, title = {Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distribution}, url = {http://eudml.org/doc/219099}, volume = {22}, year = {1994},}

TY - JOURAU - Kühne, WolfgangAU - Neumann, PeterAU - Stoyan, DietrichAU - Stoyan, HelmutTI - Pairs of successes in Bernoulli trials and a new n-estimator for the binomial distributionJO - Applicationes MathematicaePY - 1994VL - 22IS - 3SP - 331EP - 337AB - The problem of estimating the number, n, of trials, given a sequence of k independent success counts obtained by replicating the n-trial experiment is reconsidered in this paper. In contrast to existing methods it is assumed here that more information than usual is available: not only the numbers of successes are given but also the number of pairs of consecutive successes. This assumption is realistic in a class of problems of spatial statistics. There typically k = 1, in which case the classical estimators cannot be used. The quality of the new estimator is analysed and, for k > 1, compared with that of a classical n-estimator. The theoretical basis for this is the distribution of the number of success pairs in Bernoulli trials, which can be determined by an elementary Markov chain argument.LA - engKW - n-estimator; simulation; silicon wafer; Markov chain; binomial distribution; spatial statistics; -estimator; number of success pairs; Bernoulli trialsUR - http://eudml.org/doc/219099ER -